I took the steps, and changed an item's colour. I saved it as a new file and back at photoshop this little window appeared: PNG Options Interlace: None
Interlaced
So I had to choose between None and Interlaced but I'm note sure I understand what it means.
Thanks for the tutorial!

Oh My Goodness! I am so happy to have stumbled upon this solution. I have fought this problem many, many times (without success) because I was trying to change the "opacity" rather than the "lightness". Obviously, that just doesn't work, so I am extremely thankful to have this tip about using the lightness slider!